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Find the least number which when divided by15, 21, 24 and 32 leaves the same remainder 2 in each case.
- a)3362
- b)3360
- c)3456
- d)3266
- e)3364
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Find the least number which when divided by15, 21, 24 and 32 leaves th...
Step 1: Find the LCM of 15, 21, 24, and 32
To find the least number that leaves a remainder of 2 when divided by 15, 21, 24, and 32, we need to find their least common multiple (LCM).
The prime factors of the numbers are:
- 15 = 3 * 5
- 21 = 3 * 7
- 24 = 2 * 2 * 2 * 3
- 32 = 2 * 2 * 2 * 2 * 2
Now, find the LCM by taking the highest power of each prime factor:
LCM = 2^5 * 3^1 * 5^1 * 7^1 = 3360
Step 2: Add the common remainder to the LCM
Since the number leaves a remainder of 2 when divided by each of the given numbers, we need to add this common remainder to the LCM calculated in step 1.
3360 + 2 = 3362
Therefore, the least number that leaves a remainder of 2 when divided by 15, 21, 24, and 32 is 3362, which corresponds to option A.
To find the least number that leaves a remainder of 2 when divided by 15, 21, 24, and 32, we need to find their least common multiple (LCM).
The prime factors of the numbers are:
- 15 = 3 * 5
- 21 = 3 * 7
- 24 = 2 * 2 * 2 * 3
- 32 = 2 * 2 * 2 * 2 * 2
Now, find the LCM by taking the highest power of each prime factor:
LCM = 2^5 * 3^1 * 5^1 * 7^1 = 3360
Step 2: Add the common remainder to the LCM
Since the number leaves a remainder of 2 when divided by each of the given numbers, we need to add this common remainder to the LCM calculated in step 1.
3360 + 2 = 3362
Therefore, the least number that leaves a remainder of 2 when divided by 15, 21, 24, and 32 is 3362, which corresponds to option A.
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Community Answer
Find the least number which when divided by15, 21, 24 and 32 leaves th...
It will be the LCM of these numbers + 2
So 3360 + 2
So 3360 + 2
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Find the least number which when divided by15, 21, 24 and 32 leaves the same remainder 2 in each case.a)3362b)3360c)3456d)3266e)3364Correct answer is option 'A'. Can you explain this answer?
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